The Hunter's Moon and Harvest Moon are not brighter, bigger, or yellower than during other times of the year. But all full moons have their own special characteristics, based primarily on the whereabouts of the ecliptic in the sky at the time of year that these moons are visible. And the full moons of September, October and November as seen from the northern hemisphere often seem larger and brighter
In general, the moon rises about 50 minutes later each day, as it moves in orbit around Earth. All full moons rise around the time of sunset. The Harvest Moon and Hunter's Moon are special because the time of moonrise on successive evenings is shorter than usual. In other words, the moon rises more like 30 minutes later, from one night to the next, as seen from about 40 degrees N. latitude, for several evenings around the full Hunter's or Harvest Moons.
The sky remains brighter, for longer and was used by hunters to track their preyn.
The reason for the shorter-than-usual rising time between successive moonrises around the time of the Harvest and Hunter's Moon is that the ecliptic - or plane of Earth's orbit around the sun - makes a narrow angle with respect to the horizon in the evening in autumn.